How do I use Grease pencil fill tool so that it doesn't bleed out of an area?
Firstly, make sure you have a material setup that has the "Fill" option enabled (ticked) and that its Alpha is set to any value above "0". Then, if it keeps bleeding off, while still in Draw mode, hold down ALT and draw 'invisible' lines to cap any gaps in your line work. Then just click to fill.

If the problem persists, I've found that you'd need to be on the same layer and select the strokes via Object mode. However, I did run into an issue where the fill will not line up with the stroke in the same 3D space. 

Alternatively, if you don't need the fill as a separate object, you can adjust your material and just enable the "Fill" option. You can select individual strokes with edit mode and assign a specific material to whichever stroke you've selected.